# Properties

 Label 2112c Number of curves 2 Conductor 2112 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2112.c1")

sage: E.isogeny_class()

## Elliptic curves in class 2112c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2112.c2 2112c1 [0, -1, 0, 11, -11]  192 $$\Gamma_0(N)$$-optimal
2112.c1 2112c2 [0, -1, 0, -49, -47]  384

## Rank

sage: E.rank()

The elliptic curves in class 2112c have rank $$1$$.

## Modular form2112.2.a.c

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - 2q^{7} + q^{9} - q^{11} + 2q^{13} + 2q^{15} + 4q^{17} + 6q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 